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Question
Evaluate the expression without a calculator :
1. log 4 64
2. log 5 ( 1/25)
3. log ½ 16
4. log 3 243
5. log 7 1
Solve the equation for x :
6. log 6 x = 3
7. log 11 121 = x
8. log x 16 = 2
Find the x-intercept and y-intercept of the graph of each function. State as
ordered pairs :
9. f(x) = log 2 x – 4
10. f(x) = log 5 x
Use a calculator to evaluate. Round correct to 4 decimal places.
11. ln 23.5
12. ln 147
Evaluate the expression without a calculator :
1. log 4 64
The problem is 4^x = 64, and that is 3 since 4^3 = 64.
Using a calculator, take ln(64)/ln(4).
2. log 5 ( 1/25)
The answer is -2, since 1/25 = 5^-2..
Using a calculator, take ln(1/25)/ln(5).
3. log ½ 16
The answer is -4, since (1/2)^-(1/4) = 2^4 = 16.
Using a calculator, take ln(16)/ln(0.5)
4. log 3 243
The answer is 5 since 3^5 = 243.
Using a calculator, take log(243)/log(3).
5. log 7 1
The answer is 0 since anything to the 0 is 1.
Using a calculator, take log(1) / log(7).
Solve the equation for x :
6. log 6 x = 3
Take both sides as an exponet on 6.
6^(log 6 x) = 6^3.
On the left side, the functions are inverses of each other and the answer is x. On the right sides, 6*6*6 = 216.
7. log 11 121 = x
It is known that 121 = 11^2, so lot 11 121 = 2.
8. log x 16 = 2
It can be said that x^2 = 16, so x is + or - 4.
Find the x-intercept and y-intercept of the graph of each function. State as
ordered pairs :
9. f(x) = log 2 x – 4
It is known that the log 2 2 = 1 and log 2 1 = 0.
It is also known that x can't be negative.
The curve log 2 x slopes up and adds one to its height for every time that x doubles, but you need to subtract 4 from this.
10. f(x) = log 5 x
At x = 1, the curve is at 0. At x = 5, the curve is at 1.
At x = 0, the curve is at minus infinity.
Every time the x value is multiplied by 5, the curve doubles.
This means at 25 it is 2, and 125 it is 3, at 625, it is 4, at 3125 it is 5, etc.
Use a calculator to evaluate. Round correct to 4 decimal places.
11. ln 23.5
Put 23.5 in the calculator and push the ln button,
not the log button.
12. ln 147
Put 147 in the calculator and push the ln button,
not the log button.
To make sure the right button was being pushed, try ln 2.71828 and press the same button. The answer should be 0.9999...
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Answers by Expert:
Scott A Wilson
Expertise
I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?
Experience
Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later.
I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman.
I tutored at Mathnasium for well over a year.
I worked at The Boeing Company for over 5 years.
I received an MS degreee in Mathematics from Oregon State Univeristy.
The classes I took were over 100 hours of upper division credits in mathematical courses such as
calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more.
I graduated with honors in both my BS and MS degrees.
Past/Present Clients: College Students at Oregon State University, various math people since college,
over 7,500 people on the PC from the US and rest the world.
Publications
My master's paper was published in the OSU journal.
The subject of it was Numerical Analysis used in shock waves and rarefaction fans.
It dealt with discontinuities that arose over time.
They were solved using the Leap Frog method.
That method was used and improvements of it were shown.
The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.
Education/Credentials
Master of Science at OSU with high honors in mathematics.
Bachelor of Science at OSU with high honors in mathematical sciences.
This degree involved mathematics, statistics, and computer science.
I also took sophmore level physics and chemistry while I was attending college.
On the side I took raquetball, but that's still not relevant.
Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State.
I was in near the top in most of my classes. In several classes in mathematics, I was first.
In a class of over 100 students, I was always one of the first ones to complete the test.
I graduated with well over 50 credits in upper division mathematics.
Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions,
and several people every day on the PC, and you're probably make one more.
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